The BHS store in Surrey Quays will be shut by August 20 along with other stores nationwide, contributing to a loss of 11,000 jobs.
The announcement by administrators Duff and Phelps comes after they failed to find a potential buyer for the struggling retail chain.
BHS fell into administration earlier this year after its £571m pension deficit started to take its toll on the business.
Dave Gill, Usdaw National Officer, said: “This announcement is the final hammer blow to BHS staff, who have been worried about their future for over a year since the company was sold for £1 and more recently put in the hands of the administrators. Following the news that all remaining BHS stores will be closed by August 20, Usdaw calls on the administrators to redouble their efforts in finding a buyer for the remaining stores and to secure as many jobs as possible.”